Remember bandpass filters such as the IF strips in TV sets and the sweeep generators/scope setup needed to align them? Even an AA5 AM radio had multiple back-and-forth retweaks to get the oscillator to match the dial markings and the RF front end to track the oscillator. On a multi-band radio this was a real undertaking.
I once designed a product that had 7 tweaks - per channel. There were 6 channels on the pcb = 42 tweaks altogether. Fortunately they were not interactive. I could tune one up in 20 minutes, the production techs took 2 hours.
What you describe is like tuning a guitar when you put in a new set of strings. When you remove the strings, the neck will relax. As you install new strings and tune them, they pull on the neck, each one adding force so you have to go back and re-tune 2-3 times. Then the strings stretch and you have to tune yet again.
Generally, it's best to reomve and replace one string at a time so the neck only relaxes a little.
@Bill, once the strings are stretched, you can tune them without interaction. that takes a day or two. It also depends on how you play. If you play a blues-style with lots of pulls and bends, the strings will go out of tune more rapidly than if you play a classical style.
That's cheating! It does the tuning with DSP--even worse. OK, I admit that I use a tuner to tune my acoustic, which is also cheating. I really should learn to tune by ear. Well, I do, by listening to beats. that gets thr strings in tune with each other, but if the first string was sharp or flat, they re all sharp or flat but together.